Dynamic evolutionary model based on a multi-sampling inherited HAPFNN for an aluminium electrolysis manufacturing system☆
Introduction
In recent years, electrolytic aluminium products [1] have been widely used in aerospace, transportation, construction, machinery manufacturing and other significant fields and have played a crucial role in the development of the international industry [2]. Notably, the DC power consumption is quite high in aluminium electrolysis manufacturing systems (AEMSs). The research on energy saving technology [3] of AEMS has become a popular direction in the optimization of the electrolytic aluminium industry.
At present, the main ways to reduce the power consumption in an AEMS are as follows: (1) Improve the process equipment of AEMS [4], [5], [6], [7], [8]. For example, Allard et al. [4] established an improved heat transfer model of the top of aluminium electrolysis cells. The device used for handling electrolysis cell equipment to produce aluminium by igneous electrolysis was invented by TISON [5]. (2) Use the theories of intelligent modelling and decision parameters optimization to establish the accurate process model of AEMS. Then, employ the model to find best process design parameters without changing the hardware equipment in the AEMS. The fuzzy algorithm proposed by Chen et al. and Yue et al. transformed the qualitative problem of decision parameters into quantitative problems [9], [10] and was used to identify and monitor the state of an aluminium electrolysis cell. Liu et al. adopted the quasi-Z-source network [11] to establish a hybrid power supply system for the aluminium electrolysis industry, and Yi et al. [12] used a recurrent neural network, performed information-based aluminium electrolytic modelling, and optimized the method via a machine learning algorithm [13]. A multi-objective optimization algorithm proposed by Yi et al. [14], [15] was used to optimize the decision parameters in the aluminium electrolysis process.
The above two methods are beneficial for improving the performance of an AEMS. However, note that the first method, which involves improving or developing new production equipment, is difficult, requiring a large amount of capital and technical support, and is more suitable for new industrial and mining enterprises. Under the condition of existing production equipment, the second method explores the optimal process decision parameters and realizes optimal process control using intelligent optimization design theory, which can largely reduce the electrolytic power consumption and the energy cost. The latter method is therefore a very popular energy-saving technology for enterprises. The premise of using this technology, however, is to establish a dynamic optimization model [16], [17] that accurately reflects the operation principles in an AEMS. This model can centrally analyse various complex decision variables affecting the aluminium electrolysis process, reduce data redundancy, and realistically reflect the internal relations between operating parameters and power consumption. It is difficult to quantitatively analyse the mechanism of the manufacturing system due to the characteristics of an AEMS, such as multiple parameters, dynamic evolution, non-Gaussian distributions and a series of complex physical and chemical reactions in the system. Therefore, it is also quite hard to establish a prediction model that can accurately evaluate the real-time power consumption in an AEMS, which inevitably brings enormous challenges to design optimization.
Under the condition that the mechanism of AEMS is ambiguous, neural network (NN) modelling method is an effective approach to address it. This method does not need to know the complicated internal mechanism of manufacturing system and can obtain the mapping relationship between decision variables and energy consumption only by learning and training series of process data. Moreover, NN modelling is also suitable for the processing of large-scale and parallel mode problems. Therefore, the NN model has been widely used in the modelling and optimization of aluminium electrolysis. Li et al. [18] illustrated the multi-fault diagnosis of aluminium electrolysis based on modular fuzzy NNs. To achieve low power consumption and high efficiency in aluminium electrolysis, an aluminium electrolysis model and optimization method based on a recurrent NN and preference information were proposed by Yi et al. [15]. Zhou et al. [19] used a general regression neural network to predict the anode effect of aluminium electrolysis.
However, the weights remain fixed after training. When the conditions of aluminium electrolysis change, the BPNN’s weights cannot be adjusted by the new data unless another new BPNN model is retrained, but this is not a true “dynamical adjustment”. The “dynamical adjustment” in this paper is to adjust or update the weights and thresholds dynamically using the new data coming in based on the established model, instead of retraining a new model as the traditional NN does. In addition, as the statistical characteristics of process noise may not satisfy the Gaussian distribution in practical aluminium electrolysis applications, so the prediction model established by BPNN or other methods may have a significant deviation from the real model of the manufacturing system. If the predictive model with a large deviation is used to carry out process optimization design, it will seriously affect the optimization effect of the manufacturing system.
Inspired by particle filtering theory [20], [21], the conditional distribution of BPNN’s discrete weights can be obtained approximately by parameter probability estimation. Moreover, according to the real-time measurement data obtained by sensors and other devices, the probability distribution is constantly adjusted to update the model parameters of the NN in real-time. Finally, the resampling technique is introduced to avoid the model search from becoming trapped in suboptimal positions while using particle filtering theory to overcome the problem of non-Gaussian process noise statistical characteristics, so that the modelling process can approximate the optimal estimation.
Based on the above analysis, the main contributions of this paper are as follows:
(1) To accurately establish the mathematical model for solving non-linear and non-Gaussian problems, we adopt the fusion of hybrid annealed particle filter (HAPF) theory and a BPNN algorithm. The BPNN’s weights and thresholds are used as the HAPF state variables, and the BPNN’s outputs are used as the HAPF measurement variables. Therefore, this paper proposes a hybrid annealed particle filter neural network (HAPFNN) nonlinear non-Gaussian modelling algorithm to solve the above problem.
(2) To reduce the negative impact from the loss of particle diversity on modelling performance, this paper presents an HAPFNN that uses a multi-sampling technique to adjust the probability distribution of particle sets to modify the data sampling range.
(3) Considering the problem of increased data storage caused by the introduction of hybrid proposal distribution, this paper uses an adaptive inheritance method to improve the processing ability of real-time data information inherited by the algorithm.
(4) Based on the above research findings, this paper systematically proposes a novel multi-sampling inherited hybrid annealed particle filter neural network (MSI-HAPFNN) algorithm and provides a detailed algorithm design process.
(5) The above-improved algorithm is applied to the modelling problem of actual industrial manufacturing systems, namely, AEMS modelling. The experimental results show that the MSI-HAPFNN algorithm can significantly improve the predictive capacity of the model.
The organization of the paper is as follows: Section 2 gives a brief description of the problems encountered in the process of aluminium electrolysis modelling. Section 3 introduces HAPF theory and proposes a theoretical construction framework and experimental procedure for the HAPFNN algorithm in detail. Section 4 introduces the multi-sampling and inheritance concepts and presents the MSI-HAPFNN algorithm. In Section 5, the algorithm is applied and verified in AEMS modelling. Section 6 provides a summary.
Section snippets
Problem description
In process industry manufacturing systems [22], it is usually required to maintain fast response performance, accurate prediction performance and excellent robustness. Although the traditional NN model can be used to approximate the performance index of the real system, the development potential of the manufacturing system model is still very large in the face of the such complex conditions.
We define a nonlinear system: where signifies the system state vector at
Hybrid annealed particle filter
The hybrid annealed particle filter (HAPF) [31], [32] is one of the typical representatives of particle filtering theory. The hybrid proposal distribution (HPD) in this filtering algorithm replaces the posterior proposal distribution (PPD) in traditional particle filter as an importance function. Compared with the PPD, the HPD has the advantages of easy weight update and simple calculation. In addition, the measurement information obtained recently is not lost, so its importance weight has a
Design and analysis of the MSI-HAPFNN algorithm
In this paper, HAPF theory [38], [39] is incorporated into the BPNN algorithm, and the HAPFNN algorithm, which can dynamically address non-linear non-Gaussian problems, is proposed. In the model updating process, since the particles with larger weights are selected multiple times, the sampling results often contain many repetition points, which leads to the abnormal sampling direction/range; And the hybrid proposal distribution (HPD) replaces the posterior proposal distribution (PPD) as an
Experimental objects
In this paper, the above algorithm is applied to an aluminium electrolytic cell based on special-shaped perforation and shaped cathode technology [48] as shown in Fig. 7 for industrial experiments. In the figure, represents the energy consumption of aluminium electrolysis. Ideally, we wish to make the energy consumption as low as possible.
The aluminium electrolysis process has many features, such as nonlinear, multi-parameters, strong coupling, time-varying delay and high noise, and many
Conclusion
In this paper, a novel framework for adaptively forecasting the power consumption of aluminium electrolysis system is proposed. Fully taking the advantage of particle filter (PF) and neural networks, a hybrid annealed particle filter neural networks (HAPFNN) is adopted by the proposed framework to perform the prediction task. To ensure the framework to be robust to the outliers in the training data, a hybrid proposal distribution with an annealed operator, which makes the noise adjustable is
CRediT authorship contribution statement
Wei Ding: Software, Validation, Writing - original draft, Writing - review & editing, Visualization. Lizhong Yao: Writing - original draft, Funding acquisition, Project administration, Writing - review & editing, Conceptualization, Methodology, Investigation. Yanyan Li: Conceptualization, Software, Supervision. Wei Long: Resources, Supervision. Jun Yi: Formal analysis, Visualization. Tiantian He: Formal analysis, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This study was supported by the National Natural Science Foundation of China (No. 51805059), Chongqing Research Program of Basic Research and Frontier Technology, China under grant (cstc2018jcyjAX0350), Achievement Transfer Program of Institutions of Higher Education in Chongqing, China (Grant No. KJZH17134) and in part by the China Scholarship Council under Grant 201802075004.
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This document is the results of the research project funded by the National Natural Science Foundation of China.